In recent years there have been many attempts to enlarge the canonical QCD
axion window, by considering UV completions of the axion effective Lagrangian
which depart from the minimal invisible axion constructions [1]}, [2]}, [3]}, [4]}. Most approaches actually focused on the possibility of modifying
the Wilson coefficient of specific axion-SM effective operators (see Ref. [5]} and Refs. therein). A most intriguing possibility consists on departing from the \(m_a\) -\(f_a\)  relation in Eq. (). Indeed axions which are heavier than the canonical QCD axion have been explored since long and revived in the last years (see e.g. Refs. [6]}, [7]}, [8]}).
In contrast, solutions to the strong CP problem with lighter axions were uncharted territory until very recently.
